maybe he was referring to this
Sukkah 42a
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A MINOR WHO KNOWS HOW TO SHAKE THE [LULAB]. Our Rabbis taught, A minor who knows how to shake [the lulab] is subject to the obligation of the lulab; [if he knows how] to wrap himself [with the tallith] he is subject to the obligation of zizith; [if he knows how] to look after tefillin, his father must acquire tefillin for him; if he is able to speak, his father must teach him Torah and the reading of the Shema’. What [in this context] could be meant by Torah? — R. Hamnuna replied, [The Scriptural verse] Moses commanded us a Law, an inheritance of the congregation of Jacob. What [in this context] is meant by the Shema’? — The first verse. If [the minor] knows how to take care of his body we may eat food that has been prepared in ritual purity though his body [touched it]; if he knows how to take care of hands, we may eat food that has been prepared in ritual purity even though his hands [touched it]. If he knows how to answer [questions on whether he touched any ritual uncleanliness], a doubtful case on his part that occurs in a private domain is regarded as unclean, but if in a public domain as clean. [If he knows how] to spread out his hands [in priestly benediction] terumah may be shared out to him in the
threshing-floors.
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on the subject
Berakoth_53B
Samuel inquired of Rab: Should one respond Amen after [a blessing said by] schoolchildren? — He replied: We respond Amen after everyone except children in school, because they are merely learning. This is the case only when it is not the time for them to say the haftarah; but when it is the time for them to say the haftarah, we respond Amen after them.
mishna brochois 3:3
Women, slaves, and minors are exempt from reciting Shema and from Tefillin and are obligated in [reciting] Shemonah Esrei and in [affixing a] Mezuzah and in [reciting] Birkat HaMazon.
it seems to me from below that the child knew how to bless before he had a full understanding (maybe someone taught him)
shulchan aruch orach haim 199.10
A child who has reached the age of understanding and knows Who is being blessed may be taken into account for /the purposes of/ combining /to say Grace/. He may combine /with grown people to complete/ either /the quorum of/ three /people for combining to say Grace/ or /the quorum of/ ten /people for doing so with mention of the Divine Name/.
Gloss: There are /authorities/ who say that /a child / may not combine / with adults/ at all /to complete the quorum for combining to say Grace/ until he is thirteen years old, in which case he is presumed to be a grown /person/ who /already/ developed two /adult/ hairs. (…) It is /in fact/ the custom /not to count a child among the number before he is thirteen years old/ and one should not depart /from it/. ...
and
shulchan aruch orach haim 55.4
There are /authorities/ who permit saying an expression of sanctification when there are nine /adult people present/, if a child who is more than six /years/ old and is aware to Whom one prays combines /with them/, but their opinion is not acceptable to the great Poskim. Correspondingly, a slave or a woman may /also/ not be combined /to complete a minyan/.
Gloss: /A child/ may not be combined /to complete a minyan/ even by virtue of a Chumash /he is holding/ in his hand. However, there are /people/ who are accustomed to be lenient /about this/ in a time of pressing /need/. (…)
maybe we look on teaching prayer as teaching torah (the prayer is part of torah halocho (mitzva))
shuchan aruch harav yora daya hichois talmud torah 1.1
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ובימיהם שהיו מספרים הרוב בלשון הקודש וגם התינוק כשמתחיל לדבר היה אביו מספר עמו בלשון הקודשכט ועל כן לא היו צריכין ללמד התינוקות פירוש המלות
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my "inaccurate" translation (follow the Hebrew link for sources)
and in those days when most people would talk in lashon hakodesh, and when the child would begin to speak his father would talk with him in lashon hakodesh, so they did not need to teach the children the pirush hamilois
shuchan aruch harav orach haim 186.3
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אבל הקטן אינו מוציא את האשה שאכלה כדי שביעה שמא היא מחוייבת מן התורה אבל מוציא הוא את מי שלא אכל כדי שביעה אפילו הוא א[יש] כיון שאינו חייב מן התורה אלא מד"ס ואפילו אם הקטן גם כן לא אכל כדי שביעה שמכל מקום הוא חייב מדברי סופרים כמותו שברכת המזון אינה דומה למגילה והלל ברכות קריאת שמע ושאר מצות שעיקרן מדברי סופרים שאין הקטן שהגיע לחינוך מוציא את הגדול לפי שהקטן מצד עצמו כשהוא עתה פטור לגמרי אלא שמחנכין אותו כדי שיהא רגיל במצוה זו ויהיה סריך כמנהגו כשיגדל לפיכך אינו בדין שיוציא את מי שהוא גדול כבר אע"פ שחיובו אינו אלא מדברי סופרים כיון שהקטן גם חיוב זה אינו חייב אלא משום להרגילו לכשיגדל שאז יתחייב חיוב זה של דברי סופרים אבל בברכת המזון מה שמחנכין את הקטן לברך אחר אכילתו לשובע כשיגדל שהוא חיוב מן התורה לפיכך כשם שהוא מוציא את הגדול שלא אכל כדי שביעה אם הוא אכל כדי שביעה כך מוציאו אם לא אכל כדי שביעה כיון שחינוכו כשלא אכל כדי שביעה מועיל לו להרגילו כמו כשאכל (ו)יותר
